I bought a "test bar", which is a 10" or so long with MT3 end.

I inserted centers in the headstock and tailstock and mounted the bar
between those. Then I aligned tailstock with headstock, such that the
position of the indicator was the same at both ends.

This gave me about 6 inches of travel along the straight portion of the
test bar.

The good news is that the travel of the indicator, as I moved the
carriage from one end to another over 6 inches of distance, did not
seem to exceed 0.0003" or so.

Of course, aligning tailstock using position of carriage as a
reference, and them measuring deflection of the indicator on carriage
using the bar as reference, is a little bit "self referential".

In other words, the indicator does not really tell me if the carriage
moves parallel to the imaginary axis of the spindle rotation, because
that axis was not used in any way. But what the indicator does tell
me, is that along those 6 inches, the carriage moves on a straight
line.

That is already something and is much better than what happened with
my old lathe, where the carriage moved along a jumpy line (as
evidenced by abrupt changes in thickness of a test cut).

I will try to do more measurements.

i